AD-AGB3 699 ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND) F/G 9/5THICK FILM MICROSTRIP BUTLER MATRIX FOR THE FREQUENCY RANGE I-ETC(U)

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00 9 Technical 04 19118sE c0

FREQUENCrRANGE 1.5-1.7 GHz.

by

Procurement Executive, Ministry of Defence* Farnborough. Hants

UNLIMITED)3j rp 80 4 28 149j

UDC 621.396.67 : 621.396.679.4 : 621.3.038.615 : 621.3.029.64 : 621.396.4:621.3.049.77-418

* ROYAL AIRCRAFT ESTABLISHMENT

Technical Report 79118

Received for printing 10 September 1979

A THICKFILM MICROSTRIP BUTLER MATRIX FOR THE

FREQUENCY RANGE 1.5-1.7 GHz

by

A. G. Tabb

SUMMARY

This Report describes the design, construction and electrical measurement

of a 4 x 4 Butler Matrix for the 1.5-1.7 GHz frequency range. The Matrix vas

constructed in thickfilm technology on an alumina substrate. A computer aided

design package was used for the circuit synthesis.Accesis on FOr

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LIST OF CONTENTS

I INTRODUCTION 5

2 THE BUTLER MATRIX 5

2.1 The broadside beam Matrix 52.2 The non-broadside beam Matrix 6

3 GENERAL MATRIX DESIGN 6

3.1 Input port numbering 63.2 Output port numbering 83.3 Phase shifter values 83.4 Design specification 9

4 CHOICE OF MATRIX COMPONENTS 10

4.1 Couplers 10

4.1.1 The Lange interdigitated coupler I!4.1.2 The Schiffman coupler I!4.1.3 The 900 hybrid coupler II4.1.4 The 1800 hybrid coupler II4.1.5 The broadside coupler 114.1.6 The Podell coupler 12

4.2 Phase shifters 12

4.2.1 The dielectrically loaded line phase shifter 124.2.2 The meanderline phase shifter 124.2.3 The loaded line phase shifter 12

5 COMPONENT DESIGN 12

5.1 Couplers 125.2 Discontinuities and fringing effects 135.3 Phase shifters 13

6 PRACTICAL DESIGN OF A COMPLETE MATRIX 15

7 THEORETICAL ANALYSIS OF THE DESIGN 16

A8 1SUREMENTS 17

8.1 Measurement of test pieces 17

8.1.1 Phase shift 178.1.2 Insertion loss 178.1.3 Return loss 178.1.4 Isolation 18

8.2 Butler Matrix measurement and measurement accuracy 18

8.2.1 Phase measurement 188.2.2 Insertion loss 198.2.3 Return loss 198.2.4 Isolation 19

9 A PRACTICAL APPLICATION 19

10 DISCUSSION AND CONCLUSIONS 20

Acknovledgments 23

co

LIST OF CONTENTS (concluded)

Appendix A Block diagram of a 32 x 32 Butler Matrix 25

Appendix B Theory of loaded line phase shifters 27Appendix C Polar diagrams of an array fed by a Butler Matrix 33

Tables 1-6 38

References 45

Illustrations Figures 1-52

Report documentation page inside back cover

aoI

91

mmI

. . . I . . . . 0 III I i . .

I ITRDUCTION 7

A Butler Matrix is a passive multiport component which when loaded with

radiating elements enables production of a beam of microwave energy in a specified

direction in space, dependent upon which input port is activated.

This Report describes the general design procedura and analysis of Butler

Matrices up to order 5 (ie 32 input and output ports). In particular it describes

the design and measurement of a 1.5-1.7 GHz, 4 x 4 Butler Matrix constructed in

microstrip on alumina by thick film technology.

2 THE BUTLER MATRIX

The Butler Matrix consists of an equal number of input and output ports

connected through an array of phase shifters and couplers such that when a signal

is applied to any input port it produces equal amplitude signals at all output

ports.

There are two main types:

2.1 The broadside beam Matrix2

Here, the signal impressed on one input gives rise to equi-amplitude equi-

phase outputs (broadside beam condition), whereas on any other input the applied

signal gives rise to equi-amplitude signals at all outputs but the phase differ-

ence between any two adjacent output ports is a function of the input port number.

It requires the provision of a -3dB coupler giving a w-phase difference between

the outputs when one input is energised and equi-phase outputs for the other input

energisation. Such a coupler is shown in Fig Ia.

For the Matrix with 2k inputs and outputs (where k is a positive integer)

the phase length between any input and output can be given by

-,+ (n -I)m2i0 2t2=

where 4, is the phase shift between input m, output n,

*0 is the phase shift from broadside m - 0 to any output,

m is the input port number -2k-I m a< 2k-I -

andn is the output port number I < n < 2k

A Matrix of this size would require a total of k2k -I couplers and

(k - 1)2k phase shifters allowing a total of 2k different beams to be radiated

simultaneously.

6

2.2 The non-broadside beam Matrix

Here, a signal applied to any input port produces equi-amplitude signals at

all output ports but with a constant phase difference between them resulting in

formation of beams at a certain angle in space. It requires a coupler giving a

w/2 phase difference between output ports for either input port energisation

(Fig Ib).

The phase difference A# between radiating elements for this Matrix with

2k input and output ports and for a scan angle e is given by3 (Fig 2a):

2wdA# -L sin e

where d is the element spacing,

6 is the scan angle,

A is the wavelength.

This type, as the broadside type, requires k2k-i couplers and (k 1)2k

phase shifters.

3 GENERAL MATRIX DESIGN

4A general design procedure is available in the literature but in this

section a somewhat simpler systematic approach is outlined for the non-broadside

beam Matrix, showing how the input and output port numbering is achieved and

giving the phase shifter values for each rank.

A systematic design approach for the broadside beam Matrix is available in2the literature

Section 2.2 explains what happens for a signal applied to a given input.

For a basic 4 x 4 Matrix array four beams are possible as shown in Fig 2b.

The beams to the left of the array axis are named first left, second left

(working away from the axis) and those to the right first right and second right.

To link the beam formed to the input forming it, the inputs are labelled IL, 2L,

IR and 2R but due to the various phasing sections of the Matrix (although

symmetric) the numbering sequence of the input ports does not run concurrently.

3.1 Input port numbering

The derivation of an input port numbering sequence for a Matrix of order

N - (2 i N beam) is an iterative process. It builds upon the numberingN2 N . k-) and sosequence derived for the Matrix one order lower beams, where 2 '

7

N =2on back to - 2 , ie four beams as starting point. The sequence for two beams

is an exception to the method but is simple enough to annotate at sight. The

examples which follow viii illustrate the method described below.

To derive the input numbering sequence for a Matrix of order N - 2 , add

2k-2 to each term of the first half of the input port numbering sequence derived2k- Ifor the Matrix of order 2 . Reverse this new sequence in pairs and interleave

k-Iin pairs with the original sequence (order 2 - ) after the first term. Append

the mirror image to this sequence and the resultant is that required for the

input port numbering of order N = 2k . The terms are then lettered alternately

R and L to relate them to the beams they produce at output.

(i) ki 1, N! -2 IR IL exception to the rule

(ii) k2 -2, N2 - 4 1 half of input port numberingsequence derived in (i) fork 1 ie k2 - Ik2-2

2 +2

1 2 interleave

1 2 2 1 mirror image

IR 2L 2R IL

(iii) k3 -3, N3 -8 1 2 half of input port numberingsequence derived in (ii) fork2 = 2, ie k3 - I

k -2

4 3 reverse as pairs

1 4 3 2 interleave

IR 4L 3R 2L 2R 3L 4R IL mirror image and add R, L

(iv) k4 4, N4 16 I 4 3 2 half of input port numberingsequence derived in (iii) fork3 =3

k -25 8 7 6 +2 4

8 5 6 7 reverse as pairs

1 8 5 4 3 6 7 2 interleave as pairs after firstterm

* IR 8L 5R 4L 3R 6L 7R 2L 2R 7L mirror and add R, L6R 3L 4R 5L SR IL

8

3.2 Output port numbering

For a Matrix of order N 2k write down the first N numbers of the normal

number sequence provided the layout is as in Fig 3.

3.3 Phase shifter values

From a design such as Fig 4, it will be seen that the number of rows of

phase shifters for an order N - 2 kMatrix is k - I and each unit must insert a

multiple of -ff/2 k radians, derived by an iterative process starting from the

values for the k4 - 4 case.

In general for the first row of phase shifters take half the sequence for

the kn - I case and repeat it. Alternately add and subtract I, ignoring zeros

for this treatment, to the half-way point in the sequence and mirror. Add to the

original sequence and mirror.

For the second row take half the sequence for the k - I case (as for firstn

row) and repeat each number 21 times multiplying each by 21, then mirror. This

gives the sequence for the second row of phase shifters.

For the nth row take half the sequence for the kn - n + I case and repeat

each number 2n-1 times, multiplying each by 2n - then mirror resulting in the

sequence for the nth row of phase shifters.

() In the case of k I no phase shifters are required.

(ii) For k2 - 2 it can be seen from Fig 3 that this case requires one rowVi of phase shifters, multiples of wi/4, arranged sequentially as:

1 0 0 1

(iii) For k3 ' 3 two rows of phase shifters, multiples of -n/8, are

required.

For the first row take the sequence for k -

1 0 0 1.

Add and subtract 1.

2 0 0 0.

Add this to the original sequence (k3 - 1) and.mirror to give the

required phase shifter values for the first row.

3 0 0 1 1 0 0 3.

From k4 - 4 onwards the method follows the iteration process described40

above.

9

(iv) k4 - 4 three rows of phase shifters, multiples of -w/16, are

required.

The first row uses half the sequence for k4 - 1, repeated.

3 0 0 1 3 0 0 1.

Alternately add and subtract 1, ignoring zeros to the half-way point

and then mirror.

4 0 0 0 0 0 0. 4.

Add this to the original sequence and mirror, giving the first row

sequence:

7 0 0 1 3 0 0 5 5 0 0 3 1 0 0 7.

For the second row of phase shifters take half the sequence for the

k4 - 1 case and repeat each number twice multiplying each by 2, then

mirror.

. 3 0 0 1

6 6 0 0 0 0 2 2

6 6 0 0 0 0 2 2 2 2 0 0 0 0 6 6.

For the third row take half the sequence for the k4 - 2 ca-- and

repeat each number four times, multiplying each by 4 and mirror.

1 0' 4 4 4 4 0 0 0 0

4 4 4 4 0 0 0 0 0 0 0 0 4 4 4 4.

Appendix A gives a complete example of the input and output port numberingand phase shifter values for an order N - 32 Matrix.

Fig 4 shows a complete basic block diagram for one half of this 32 x 32

Matrix, the other half being a mirror image apart from the output port numbering.

Note that each line of phase shifters adds up to -Nw/8 and that the -w/4

phase shifters are always at the row of couplers next to the antenna array.

Equal phase shift magnitudes are found in places symmetric to the Matrix

axis, the smallest phase shift value being -w/N.

3.4 Design specification

Below is detailed a typical design specification for a 4 x 4 Butler Matrix.- 4

10

Frequency band : 1.535-1.66 Glz

Transmit band : 1.535-1.5585 GHz

Receive band : 1.6365-1.66 GHz

Centre frequency: 1.5975 GHz

Total losses : -1.5 dB target

-2.0 dB maximum

Phase error : ±5.00 target

VSWR : 1.2 : I any input, output

Isolation : -20 dB minimum

Dimensions : no specific requirements - as small as possible

Weight : no specific requirements - as light as possible

Connectors : SMA type

Technology : suitable for space qualification.

Plus the following:

Transmission medium microstrip

Technology thickfi lm

Substrate type alumina (MRC superstrate) Er = 9.8

Maximum substrate size 50.8 x 101.6 x 0.635 m

Conductor ink Plessey EMD C5700 fritless gold

Ground plane ink Englehard T894 silver

Screen mesh size for thickfilm 325 meshes/square inch

printing

4 CHOICE OF MATRIX COMPONENTS

For the Butler Matrix there are two basic components that have to be

* selected: the hybrid coupler and the phase shifter. It will be seen below that

while one is free to select the particular type of hybrid considered to be optimum

for the task in hand, in the case of the phase shifter there are fundamental con-

siderations of dispersion which restrict the choice to some extent.

Since the chosen transmission medium is microstrip, several types of

coupler and phase shifter exist that can be used in the design, each having

various advantages and disadvantages.

4.1 Couplers

The couplers considered were:

*0

4.!.! The Lange interdigitated couplerThe Lange interdigitated quadrature hybrid coupler5 (Fig 5) has the advan-

tages of being broadband and coupling in the forward direction thus simplifying

layout procedure, requiring shorter tracks hence lower insertion loss. The

problem of decreasing directivity with increasing frequency is avoided by using

cross-strapping between alternate lines but this makes the device less robust and

more difficult to manufacture. Unfortunately no general design data have been

published.

4.1.2 The Schiffman coupler

The Schiffman coupler6 (Fig 6) is very broadband but presents design

difficulties due to the even and odd mode velocity differences in the coupled

lines.

4.1.3 The 900 hybrid coupler

This coupler (Fig 7) is relatively narrow band, couples in the forward

direction hence simplifying layout and constitutes no great design difficulties.

It has a /2-phase shift between coupled and through arms and presents a low VSWR

to the connecting circuit even when the output lines are equal but not exactly

50 ohm.

4.1.4 The 1800 hybrid coupler

The conventional microstrip rat-race has three branches of X/4 and one of

3X/4. To reduce frequency sensitivity one of the arms can be replaced by a7coupled pair of grounded A/4 lines (Fig 8) producing a w-phase shift. This

coupler has the disadvantages of diagonally opposite coupled ports and, in the

wideband version, a very narrow coupling gap and shorting holes in the substrate.

The narrow coupling gap can be overcome if the complication of a sandwich

construction can be tolerated to obtain the required mutual coupling.

4.1.5 The broadside coupler

This relatively wideband coupler providing good isolation and a straight-

forward layout is shown in Fig 9a. The coupling mechanism is special in that a

wave travelling in one direction on one of the lines couples only to a wave going

in the opposite direction on the other line. Hence the disadvantage of diagonally

opposite direct and coupled ports and a greater disadvantage of low level

coupling ( -5 dB possible with laser triming).

-1

12

4.1.6 The Podell coupler

The Podell coupler8 of Fig 9b overcomes even and odd mode velocity disper-

sion by using a sawtooth design on the inner edge. This sawtooth effectively

slowing the odd mode as it propagates along the inside edge while the even mode

remains unaffected along the outside edge. Its advantage is that its layout,

(similar to the broadside coupler), only involves thickfilm printing. Its dis-

advantages are the necessity to use tandem coupling for a 3 dB split (thus

greater insertion losses) and the coupled and through arms are diagonally

opposite, leading to complicated overall layouts. Also no design information is

available in the literature.

4.2 Phase shifters

In the explanation given in section 2 of the working of the Butler Matrix,

a spot frequency only was considered in the interests of simplicity. If however,

the Butler Matrix is to be of any practical use it must operate correctly over

the information bandwidth, ie dispersion over this bandwidth must be prevented.

To achieve this, identical phase frequency slopes must be designed into sets of

phase shifters having different electrical lengths.

The following passive phase shifters were considered:

4.2.1 The dielectrically loaded line phase shifter

This phase shifter is achieved by placing lumped constant, high permittivity

material on a uniform microstrip line. This hat, the unfortunate disadvantage of

setting up moding in the line and introducing mismatches (hence greater VSWRs).

4.2.2 The meanderline phase shifter

Meanderlines are easy to design but the line lengths necessary for a full

set of shifters (for larger matrices) causes greater insertion losses.

4.2.3 The loaded line phase shifter

Loaded line sections with short or open circuit stubs can be used to distort

the phase-frequency slope of a uniform transmission line over a narrow bandwidth.The simplest type cannot produce greater than i-phase shift unless open or shorted

stubs are used in combination.

5 COMPONENT DESIGN

5.1 Couplers

For ease of layout and design using the proposed technology the 900 hybrid

coupler of section 4.1.3 was ideally suited. For the relatively narrow bandwidth

• I " ' ..• . ..

1132

required (8%) a single section coupler was adequate and previous experience has

shown that in a square geometry this coupler performed more closely to theoretical

predictions than in a circular geometry.

The basic configuration shown in Fig 7 required some length modifications to

compensate for the somewhat unpredictable junction discontinuities involved when

two different impedance lines meet9

5.2 Discontinuities and fringing effects

In addition to the main point made in section 4.2 there is the possibility

of slight dispersion of the information frequencies by the microstrip line itself.

At the frequencies of interest and the bandwidth requirements in the specification

of section 3, errors due to this problem have been rendered insignificant by the

best compromise design. It should therefore be mentioned that the dispersive

effects of microstrip lines, although not too important at these frequencies, are

a problem in circuit design and dispersion is dependent on the permittivity of the

substrate and the physical dimensions of the lines. Its effects are noticeable

when more of the field becomes contained in the substrate thus increasing the

effective permittivity (phase velocity) and lowering the characteristic impedance

of the microstrip lines.

Effective permittivity varies across the substrate and, more so, from sub-

strate to substrate, so average effective permittivity values must be used in

calculating line lengths, these values having been measured for lines of differing

impedance.

Junction and open end effects have also to be accounted for, though again it

is not absolutely necessary at these lower frequencies.

In the Butler Matrix component design, the microstrip dispersive effects

compromised were line lengths (by using effective permittivities), junction

effects and open circuit effects.

5.3 Phase shifters

From line length considerations, ease of design layout and relatively

narrow bandwidth requirements, meanderline phase shifters were chosen in conjunc-

tion with loaded line sections. The choice of meanderlines was made primarily for

ease of layout, but it will be appreciated that this choice automatically sets the

phase frequency slope which has to be designed into the loaded lines.

In the loaded line there is a choice of open or shorted stubs but the latter

would necessitate numerous holes being drilled at various points in the substrate

14

and so, from the point of view of cost and ease of manufacture, phase shifterdesign was limited to loaded sections with open circuit stubs.

To obtain the required value of insertion phase while ensuring an identical

phase-frequency slope, each set (being the complete set of phase shifters between

any two ranks of couplers) was designed together.

Fig 10 shows a typical loaded line section and its equivalent circuit.

For any line or filter section the characteristic impedance is given by

z - - 10 scOC

sc oc

and the propagation constant y is given by

tanh(y) -- pand

Y - +jo

where a is the attenuation constant (a - 0 for a lossless network),

B is the phase constant or delay of the section vix the angle in radiansby which the current leaving the section lags the current entering it,

Zsc is the short circuit impedance (- )sc

andZ is the open circuit impedance (-yl_-).ocOc

Hence, for a lossless network

tanh(y) - tanh(jB) = j tan(B)

". B = tan [- j

Appendix B gives a detailed solution of the phase-frequency slope problem of

section 4.2 in terms of the normalised admittances of the lines and stubs, the

phase shift of a section at midband and the change of this phase shift with fre-

quency (the phase slope). An equivalence is made between this phase slope andtODj that produced by a length of transmission line of normalised admittance 1.

15

The equation of this length of transmission line and the equivalent loaded10line section are used in an iterative program to compute the desired phase

shifter design values. Hence a set of phase shifters is designed with the same

phase slope as that of a known length of meanderline. This constant phase slope

is necessary to ensure a constant phase difference between each phase shifter

over the frequency band of interest.

Typical examples of the program output are shown in Table 1.

Since, in this project, a 4 x 4 Matrix was being designed the single rank

of phase shifters required consisted of w/4 and 0 degree phase shifters. As the

phase differences, output to output, were constant for each input stimulus, and

all output phases were relative to the IR, I plane of the Matrix, the phase shift

values need not necessarily have been identically w/4 and 0 degrees. Provided

there was a w/4 phase difference between them, any pair of the set shown in

Table I could be used.

For ease of layout on a 101.5 x 50.8 mm substrate (the largest processable)

the 1350 meanderline and 900 loaded line sections were chosen.

The basic configuration of these phase shifters had to have some length

modifications to the values given in Table I to compensate them for the open

circuit and junction effects of microstrip lines.

6 PRACTICAL DESIGN OF A COMPLETE MATRIX

As can be seen by comparing the Matrix schematics of Figs I and 11 there

was a physical layout problem for Matrices of greater than order N - 2 due to

their non-flat nature especially since the chosen transmission medium was micro-

strip. The configuration as it stood, required crossover lines which in any

adverse environment would have introduced reliability problems besides increased

complexity in the thickfilm processing.

Fig 12 shows a compromise situation, suitable only for the Matrix of order

N - 4, where the circuit was orientated in such a way that no crossovers were

required and the circuit was purely of flat geometry. Although the circuit now

had no crossovers and was straightforward to produce, it had the disadvantage of

having inputs diagonally opposite each other and also outputs opposite each other

on the other diagonal.

Because of the limited size of substrate available for processing soe

thought was given to the actual positioning of the components on the substrate.

cc,

16

In order to keep the surface area taken up by the meanderline to a mnimm

it had to be folded while maintaining a minimum separation between lines, to pre-

vent cross-coupling, and a minimm bending radius, to allow the centre line to be

taken as the correct electrical length. It was also necessary to maintain a

minimum separation between the tranmission lines and adjacent loaded line

sections to prevent any possible interaction.

Additional lengths of 50 ohm line used for joining sections together had to

be the same length in each part of the Matrix either input or output section, but

not necessarily both, although it did simplify the design. For the practical lay-

out, see Fig 13.

Connection to the external circuit was by SMA connectors (type OS14 14107A)

between which a minimum distance had to be maintained to facilitate connection

and disconnection of external apparatus. These connectors used pressure contact

with the microstrip line in the breadboard models.

The printed, dried and fired substrate was mounted on an aluminium block to

facilitate connection of the SMA connectors. To ensure adequate grounding

between the substrate ground plane and the mounting block the circuit was stuck

to the block using DAG, a silver loaded ink. This grounding method produced more

consistent results than using other grounding materials. It also had the added

advantage of inhibiting movement of the circuit under the pressure contact

connectors when it was being handled.

Fig 14 shows the finished breadboard model.

7 THEORETICAL ANALYSIS OF THE DESIGN

Using an in-house microwave analysis program, REDAP38, available on the RAE

computer the basic circuits were analysed.

Table 2 shows an example program for the phase shifters on the test circuit

the outputs being insertion gain, insertion phase and VSWR which are shown plotted

in Fig 15. It must be noted that this program was for ideal lossless transmission

lines although some allowance was made for effective permittivity of the substrate

for different impedance lines.

Loss in the line could be allowed for, each impedance requirilg its own

attenuation factor in dB per metre, though this would not affect the insertion

phase and would not add a significant amount (only 0.1 dB) to the insertion loss.

The line lengths used were exactly the same as those on the test circuit

but no allowance was made for the SA-ucrostrip transitions because of their

virtually unknown effects.

17

The coupler test circuit was synthesised similarly and results plotted in

Figs 16 and 17.

The final design of the Matrix was tackled in much the same way, the

complete program being shown in Table 3. The computed phase shift, insertion

loss, isolation and VSWR are shown plotted in Figs 18 to 22 for the actual design.

8 MEASUREHENTS

Using a Hewlett Packard network analyser a full set of RF measurements were

made on two test substrates containing the 900 hybrid coupler and the two phase

shifters, and also on two samples of the breadboard Butler Matrix. Measurements

were made at selected spot frequencies over the range 1.5-1.7 GHz.

8.1 Measurement of test pieces

8.1.1 Phase shift

The apparatus setup was as shown in Fig 23. It was calibrated for zero

phase shift through the IR, I ports of the coupler at the centre frequency of

1.5975 GHz and then the phase shift for the other output port was measured

relative to this. Next the phase shifts for input IL to both outputs were

measured. All outputs not connected to the test gear were terminated in 50 ohm

loads. Fig 24 shows the phase shifts versus frequency for the coupler.

For the phase shifters, the 900 loaded line section was taken as the zero

reference for setting up and hence the 1350 meander line phase-frequency response

is shown relative to this in Fig 25.

8.1.2 Insertion loss

This was measured using the same setup as for phase with the exception that

the apparatus was calibrated for zero dB before inserting the circuit under test.

In this way all effects monitored during test were due to the actual circuit

itself (and connectors), thus the insertion loss of the 90 hybrid coupler was

not taken relative to the -3 dB split inherent in the device.

The phase shifters were also measured for insertion loss versus frequency.

Figs 24 and 25 show the insertion loss versus frequency for the coupler and

phase shifters respectively.

8.1.3 Return loss

Return loss was measured with all output ports correctly terminated in

50 ohm loads and is shown in Figs 26 and 27 for the coupler and phase shifters

- respectively. Return loss is related to VSWR through the expressions

18

VSWR -I + 1I17 - 77l

where 1 P =log (0.05 x return loss)

the correspondence of VSWR being shown on the curves.

8.1.4 Isolation

This parameter was measured versus frequency for the 900 hybrid coupler

between each input, both outputs terminated in 50 ohm loads. Results are shown

in Fig 24.

All these measurements were made prior to the design of the complete Matrix

to ensure that the required results were being obtained. Table 4a&b summarises

these results for the transmit band centre 1.54675 GHz, centre frequency

1.5975 GHz and receive band centre 1.64825 GHz.

8.2 Butler Matrix measurement and measurement accuracy

8.2.1 Phase measurement

The same apparatus setup was used as for the test pieces. The phase shift

for each input to all output ports was measured relative to the IR, I ports which

were used for calibration of zero phase at the design centre frequency. Shown in

Figs 28 to 31 are the phase shifts through the Butler Matrix for each input to

all outputs.

Table 5 shows the ideal design values of phase compared with the actual

measured values for the complete Matrix; the 45 difference is relative and can

be ignored.

Accuracy of phase measurement was difficult to assess since non-

repeatability of the transitions microstrip-SMA connector and SMA-coaxial line

had significant effect on phase rather than on amplitude.IIt was noted that the least discernible bending of the flexible cable

produced ±0.80 change in phase and during measurement calibration was checked

regularly and was correct within ±20. Assuming ±30 for non-repeatability of

connections the total expected accuracy of the phase measurement was ±t5.80.

", 1*

19

8.2.2 Insertion loss

Again the setup was as before but was calibrated with the test circuit

omitted from the apparatus. Thus insertion loss was not measured relative to the

-6 dB split due to the Matrix couplers.

Figs 32 to 35 show the typical results obtained.

Bearing in mind that connections had to be made and broken a number of

times for each set of readings, errors of ±0.5 dB could have occurred. Checking

zero at intervals during measurement gave errors of ±0.3 dB and flexing of the

cable ±0.1 dB so total accuracy on insertion loss measurements was probably

within ±1.0 dB.

8.2.3 Return loss

Fig 36 shows the measured return loss with all output ports of the Matrix

50 ohm loaded. Also shown is some measure of the VSWR.

Here accuracy of measurement was not great for reasons mentioned before

which affected the matching, especially the SMA-microstrip transitions which

represented unknown and unmeasurable errors. No test through the connectors and

leads alone was made to assess residual VSWR and hence return loss errors,

because this would only have taken account of inserting one particular length of

line in place of the Butler Matrix.

Results are thought to be accurate to within ±1.5 dB for the lower levels

of return loss but may be ±4 dB at the higher levels, (30 dB return loss say).

8.2.4 Isolation

This parameter versus frequency is shown in Figs 37 to 40 for the bread-

board Matrix. Apparatus setup was as before and the Matrix was correctly termina-

ted at all non-used ports. Accuracy of measurement was probably within those of

section 8.2.3.

9 A PRACTICAL APPLICATION

An application for this Butler Matrix is as a submatrix for a 16 x 16

Matrix which could be part of the feed system of a satellite borne steerable beam

phased array of radiators allowing complete earth coverage.

As a first step this 4 x 4 submatrix was packaged and its performance

measured with a small planar array of four circular microstrip radiators. The

basic layout of the array in block form is shown in Fig 41. The array was

designed to operate at 1575 Mz with both left hand and right hand circular

20

polarisation. The complete array was backed by a square of RAM (radio absorbent

material). Measurements of the radiation patterns were made at the Antenna Test

Range, Lasham, using a RDC polarised helix antenna as the receiving element with

the array excited with RHC polarisation.

First, however, to qualify the array the radiation pattern of a single

element disc antenna similar to those used in the array was measured (Fig 42).

From this polar diagram it can be seen that no attempt has been made, at this

stage, to minimise the ripple around the pattern apart from verifying it is

usable. Other polar cuts show the pattern to be roughly a solid of revolution.

Fig 43 shows the basic setup of the Matrix fed array and Fig 44, the range

setup for polar radiation pattern measurements.

The radiation patterns are taken with each Matrix input being excited

individually, all others being terminated in their characteristic impedances.

The rotating pole upon which the array is mounted is then turned through 3600,

while the radiation pattern is plotted.

Figs 45 to 48 show these resultant polar diagrams. The dependence of beam

steering on which Butler Matrix input was excited can be seen clearly and

from Appendix C all beam nulls will be seen to occur at certain common angles

with the main beam peaks occurring near to one or other of these same common

angles.

In Appendix C the polar diagram for an array fed by a Butler Matrix is

calculated and a comparison is made between some ideal basic parameters to be

obtained from such a beam forming technique and the corresponding measured values.

Reasonable precautions were taken over the array dimensioning and angular

measurements on the Lasham Range, and the beam aiming discrepancies of the results

have been largely accounted for in theory.

10 DISCUSSION AND CONCLUSIONS

The most noticeable differences between the computed and measured responses of

the test pieces and Matrix breadboard models were the different phase slopes of

the plots. One reason not already mentioned was that the REDAP Analysis Program

only synthesised the actual circuit on the substrate; no allowance was made for

either the extra length of coaxial line used on the input to facilitate measure-

ment or the microstrip-SMA transition or indeed the SMA connectors themselves

which would alter the phase frequency slope of the circuit and in some respects

A the other measurable parameters.

K, 21

The network analyser could itself be set up with an initial phase frequency

slope, this not invalidating any of the phase results obtained since they were

all of a relative nature.

Omission of the attenuation factor in the REDAP progrm would not affect

the phase responses and would only slightly increase values of insertion loss and

isolation (only -0.1 dB).

The phase shifters had a measured insertion loss of <0.25 dB and a VR

<1.3 :1 (compared to a computed value of <1.2:1) over the 1.535-1.66 GHz band of

interest.

Computer analysis of a component would ideally only produce an accurate

prediction of a device's performance if access was available to a complete data

set relating to that component and its precise mode of operation. Since the REDAP

macro itself was not equipped for dealing with them in any way, the junction

effects entered in the program were dealt with as an increase in line length,

hence the computed isolation and return loss for the coupler (Figs 16 and 17)

peaked at a frequency lower than the design centre frequency.

The -3 dB power split of the coupler was not quite achieved but was within

the tolerance level of -3 ± 0.25 dB over the band of interest. Computed VSWRs

were <1.25:1 over the band and were measured at <i.22:1. A good VSWR was to be

expected in this coupler because the power reflected goes to the isolated port

and is absorbed.

For the breadboard Matrix, discrepancies occurred between the responses of

some input and output port combinations that should ideally have been identical,however these were within expected tolerance levels. Most significant was theinsertion loss for the 2L, 3 and 2R, 2 ports at the low frequency end (Figs 33

and 34). These results were re-checked a month later and found to be within

0.2 dB of the original measurement.

Table 6 summarises errors in phase shift (measured and computed) relative

to the ideal values (shown in Fig l1b) for the various input and output port

combinations. Small transmission-line discontinuities which could give rise to

significant reflections and transmission losses usually presented a very small

phase shift to the circuit.

Isolation was more critically dependent on across-the-substrate

permittivity tolerances, through the coupler changes and bad transitions.

j iMeasured isolation on all inputs was better than -16 dB, this being the worst

case at the lower band-edge. The computed value being -20 dB.

22

Insertion loss was <1.2 dB for all the input-output port combinations

measured, in most cases being <0.8 dB. The computed value was <0.25 for the

ideal circuit.

The shape and magnitude of the return loss curves could have been affected

by the input and output connectors and the connections themselves. VSWRs for all

inputs were <1.5:1 over the band of interest (this being the worst case value)

compared with a computed value of <1.25:1 for the ideal Matrix.

The VSWR given in the design specification (section 3.4) may have been a

little optimistic for thickfilm microstrip, the transitions and the cables used

in the measurements.

As an exercise in basic design principles the Butler Matrix described

largely met its specification (albeit a general rather than a specific

requirement).

Improvements could possibly be achieved by accurate prediction of the

junction effects between differing impedance lines but there is a shortage of

accurate data available on general microstrip discontinuities and connector-

microstrip transitions.

A more realistic computer prediction would have been obtained if attenuation

factors for the various lines had been used in the program (typically 2.5-3.5 dB

per metre for 33 ohm and 50 ohm microstrip lines respectively, using Plessey C5700

gold conductor paste).

Section 3 gave an example of how complicated Butler Matrix design could

become for greater than order 4, especially from the layout point of view.

Larger Matrices must, of necessity, be made up of an assembly of 2 x 2 or 4 x 4

submatrices with transmission line crossovers made externally.

A second difficulty in larger Matrix design is the large numbers of

measurements to be made during final electrical testing. As an example O , for a

16 x 16 Matrix the following measurements are necessary per frequency: 16 measure-

ments of VSWR, 240 of input to input isolation and 256 each of input to output

insertion loss and phase shift, making a grand total of 768 measurements per

frequency, each taking approximately one minute.

With the Matrix used as a feed to a breadboard four element planar array the

parameters obtained from the polar radiation patterns measured at Lasham on the

Antenna Test Range appear to be in good agreement with the ideal parameters of

Appendix C. OD

23

The array had not been optimised in any way but the ripples around the

polar diagram of the single disc element were considered acceptable, however this

hampered the fitting of a theoretical curve to the measured patterns when trying

to predict beam aiming.

The nulls and crossovers and to a lesser extent the peaks of the beams

occur at the anticipated positions and the dead ahead crossover levels are in

good agreement with the ideal.

Appendix C shows that an asymmetric lobe is to be expected whose maximum

will differ slightly in angle from the in-phase angle (which would give a maximum

for isotropic sources). Hence, the angles between -3 dB or -10 dB points cannot

be bisected to determine the angle of the lobe maximum.

However it must be noted that the null angle due to phasing is independent

of the element patterns and should therefore provide a check on the accuracy of

the element spacing and the phasing of the Butler Matrix. Alternatively a check

can be made by curve fitting to the measured element pattern and substituting this

expression for cos e in the array pattern of Appendix C.

Acknowledgments

The author would like to thank the Space Department Drawing Office for

preparing the artwork, Mr A.G. Millet and Miss D. Carver for fabrication of the

circuits, Mr M. Sidford (R & N) for permission to use the radiation patterns of

the planar array fed by the breadboard Matrix and Mr R.W. Hogg for many

k :stimulating discussions.

25

Appendix A

BLOCK DIAGRAM OF A 32 x 32 BUTLER MATRIX

The following procedure is an example of input and output port numbering

and calculation of phase shifter values for a 32 x 32 Matrix. The Matrix consists

of 5 rows each of 16 couplers and 4 rows each of 32 phase shifters.

A.1 Input port numbering

k5 - 5, N5 - 32.

Half series for k - I from section 3.1 (iv):5

1 8 5 4 3 6 7 2

k5-2+ 2 viz 8:

9 16 13 12 11 14 15 10

reverse as pairs:

16 9 12 13 14 11 10 15

interleave with original half series in pairs after first term:

1 16 9 8 5 12 13 4 3 14 11 6 7 10 15 2

mirror and affix R, L for complete set:

IR 16L 9R 8L 5R 12L 13R 4L 3R 14L 11R 6L 7R IOL 15R

2L 2R 15L IOR 7L 6R IlL 14R 3L 4R 13L 12R 5L 8R 9L

16R IL.

A.1.1 Output port numbering

Because of the chosen layout the first 32 numbers of the normal number

sequence are used.

A.1.2 Phase shifter values

There are four rows of shifters whose values are multiples of - w/32.

AI.2.1 First row: take half the sequence for k 5 - 1 (ie as derived for

the first row of k4 - 4 in section 3.3 (iv)) and repeat

7 0 0 1 3 0 0 5 7 0 0 1 3 0 0 5.

Alternately add and subtract 1, ignoring zeros to the half way point, then mirror.

A8 0 0 0 4 0 0 4 4 0 0 4 0 0 0 8.

26 Appendix A

Add to the original sequence and mirror.

15 0 0 1 7 0 0 9 11 0 0 5 3 0 0 13 13 0 0 3 5 0

0 11 9 0 0 7 1 0 0 15

A.1.2.2 For the second row take, as in AI.2.1, half the sequence for k -

7 00 1 3 0 0 5.

Repeat each number twice, multiplying by 2 then mirror

14 14 0 0 0 0 2 2 6 6 0 0 0 0 10 10 10 10 0 0 0

0 6 6 2 2 0 0 0 0 14 14.

A.1.2.3 For the third row take half the sequence for the k - 2 case (ie

as derived from section 3.3 (iii))

3 0 0 1 .

Repeat each number four times multiplying by 4 and mirror

12 12 12 12 0 0 0 0 0 0 0 0 4 4 4 4 4 4 4 4 0 0

0 0 0 0 0 0 12 12 12 12 .

A.1.2.4 For the fourth row take half the sequence for the k. - 3 case (ie

as derived in section 3.3 (ii))

1 0.

Repeat each number eight times, multiplying by 8 and mirror

8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 008 88 88 888S.

Appendix 2

THEORY OF LOADED LINE PHASE SHIFTERS

The A matrices* of the lossless netvork of Fig 10 are

j tan e0El0 12 0 E

IIjBY 1 I jY2 tan O2 1jBY 1 I I

1j a 82

1 -tan e2B tan2 E2

Y 2

2jBY + jY 2 tan 2 - jB 2 - tan e I- B y tanG 2 0 2

Now the short-circuit and open-circuit admittances of the network are given by

Y sc A22/AI2 (B-1)

Y A 2A (B-2)

HenceY - BY tan 6

Y = 2 1 - 2 (B-3)sc j tane

2 222

2YIY 2jBYJy2 + j 2 tan e22 - jBBY tan e2 (B-4)oc Y2 - BY tan 8 2

The characteristic admittance is then

Y - .Y Y0 oc sc

- (2BY Y2 + Y2 tan 6 B 2Y 2tan e2 Y2 -Y tan e2 B5

(Y2 BY1 tan 02) (tan 62)-5

* different from Butler Matrix

28 Appendix B

Normalising to Y0 , and letting YI Y2 be the characteristic admittances of

1V Y2 normalised to Y0 and Bnorm - tan 61 - I for A/8 stubs, (B-5)

becomes

2 y 2 tanG V12 Y 2 2 tan 62

tan 82

But tan 62 - " for A/4 line

y2 y (B-6)

Also

tan = (from section 5.3)Yac

-j Y j Y 2 + y tan e2 - B2y2 tan e2 tan 62

-17 BY1 tan e2 )2

Normalisiug to Y0 and letting tan 62 2

'.1 y2 yj tan -j 2

Z. tan8 =,+

YI

. - tan-'[ ,] (B-8)

LL

Appendix B 29

Now from (B-7) and putting B - tan 1 for open circuited stubs where 20 6211 2

2a +y 2 tan22 tan 2 y2 tan2 O0tan 2 tan 2 2 2 11 2

(Y2 - yl tan 9 tan 62)

2tand putting t = tan 81 2 tan 2e= tan 02

- I

1 2 t22 2

"2Y1 t2n Y +t t Y I4

tan1- 2 1 (. 2 2 2I -

Y 2(I- t 2) 2Ylt2

tan W (B-9)

; Now

do dO dx dt dI (-0

For midband t I and normalising

dxI I +! 2 y

2 1

2

I-t

dt(I 2B-tYI

- an-() (-9.. .. .. . . . . . - .. ... . . .. .. . . .. ... ... .. .. .... I i l l .. .. .. ]1. .. . . . . . . . ..N o. . .. ... .. . . .. .. . . . . . . . .....

30 Appendix B

S3 2 32rx(2 2Y It 2 (2t. - 4t + 2tY 2 4t 4 3 Idt [ t(~2)y,:2y 2 _ t4y 2 ( -t2) -2Y, t2)2

L 2 t2( - t2) 1 2 + t2Y2 - t4Y(- 2tY2 - 4tY1)]

2 - t2) _ 2Yt 2)

At uidband and normalising

dxl r-2Y,(- 2Y1Y2 + 2Y2 - 4Y~ 2 Y7Y( 2 Y2 + 4ITF1,., y2 _ y2c- ,,4Y2i I 27 - 2

4Y Y2 -+ 4Y3 I 8Yy 21 2 2 1 2

d_, - I + n2l

Vj y2 + y312 2-

y2 y: dxl 2 1 + 2 (d- 12)

2 1

dt2I I+tan1

-O at midband and norumalising .(B- 13)

Appendix 3 31

Assuming air is the dielectric for simplicity, for the stub

2n I 2wl1fe

C

de 21rl=" 1- (B-14)

where c is velocity of light in vacuo.

Hence, from equations (B-10), (B-1l), (B-12), (B-13) and (B-14)

yY 2 y +Y WirdB_ 1 2 1 2 .2 1

df ,2 y2 c2 1 Y 2 -Y

47 1i

Now Il for the stub A c/8 where Xc is the centre frequency wavelength

dc ( + y -ff" (YI + Y radians/Hz . (B-16)!df 2c 2) 2

c

The corresponding rate of change of phase for a piece of uniform transmissionline is

dO , 2wr , (B-17)df c

For equal rates

2,L _ c (j+ y2)

'" " T (Yi + Y2) (B-18)

is the electrical length of uniform line is

_1, .~ . (Y, + 2). (-19)

32 Appendix 3

Hence for the design of a set of phase shifters we choose Y to give us the

required phase shift in accordance with

wl~~eSm tan7 (*)I;, while

y2 -y 2 -2 1

• dO

and Y + Y is also fixed at the required phase-frequency slope T .2 1 df

:Go,ii

0

33

Appendix C

* IPOLAR DIAGRAMS OF AN ARRAY FED BY A BUTLER MATRIX

* C.1 Suppose an array of 2n omni-radiators spaced 'd' apart is fed by a Butler

Matrix with equal amplitude E and progressive phase shifts with respect to some

datum at the array centre as shown in Fig 49.

The RF signal reaching a distant receiver in the direction e will be

proportional to:

E~in t + !I d )+i~w I ldi)_ L_ sin e + sin t - n + Misinn)

+ sin t +n (2- wd sin 6

nt n+ (2n 1))

si wdsin e f w i2Esin wt cos ~- sin e) + o( 2 - sin)+

+. co+(. (2n- 1) ird sina

If the Butler Matrix makes 1' #2' f2 ' n such that the radiation adds

in phase at 6 = eP then

f * w n 3Ld sine f. (2n- I) wd sin Op.~ X sin Op , 2 X X i p, ""'

making each cos term unity and giving

3f1 (2n - 1)2 ' ' n 2 (Zn

Hence dropping the RF term sin(wt) , the distant field is given by:

34 Appedix C

24( 0 side)+ coo 3(sin ! + + cos(2n 1)(J. ! sinTc T(~ 2 A (72 - e)].-

This sunmation is easily made and becomes

2.Esin 2n(.! s in ]

2 9 sin 0)

therefore for a uniform array of 2n radiators the polar diagram is given by

E sin 2n(d " e) silk

(C-0)

sin\T-T sin/

If - 2 sin e is small (ie if d is small and *i correspondingly small,

which culminates in a distributed source array) then

\2n Tdsine dT 'n

and (C-I) becomes

E sin 2n"Ld sin 0

If we now put E where N is the total number of sources, N = 2n , thepolar diagram is given by:

sin N(4L - e)R0 lu -T sin

(C-2)

N dsin -(L)_-I c

Appendix C 35

which is of the form s xx

In this case however it is more accurate to apply (C-I) as there are 2n - 4

elements and d - A/2. The elements are not isotropic radiators and this must

also be allowed for, g if each element were a dipole having a cosine pattern

maximising at em , Fig 50, we must replace E by Ed cos(O + 0) in (C-I) and

the array pattern shape is then

sin 41-.- - sinE cos( + e) 2 2 (C-3)

(Tsn - if sine)

element array

pattern pattern

C.2 Results

C.2.I Beam peak positions assuming isotropic radiating elements occur at values

where

sin 6 7rd 2

but for the Kth beam

2K - IK = 2 1

and

2n 4

hence

sine = X 2 w (2K- I).

For K I 0 =±14.50

K - 2 =±48.60

Now, consider the case where 0 - 0 and 0 p =48.60 corresponding to

1350 phase difference between Butler Matrix outputs (where all radiating elements

add in phase) giving *I - 2.356 radians.

sin 4(1.178 - sin 0)A plot of W sine cos O in dB versus 8 is shown in Fig 51

36 Appendix C

and an expanded version in Fig 52. This shows the asymmetrical main lobe and

three side lobes. The main lobe peak is 7.40 off the in-phase angle (which would

give a maximum for isotropic sources).

Similarly if 0 - Op - 14.50, corresponding to 450 phase difference between

Butler Matrix outputs, is substituted in the above expression the main lobe in

this case peaks at 13.30 which is 1.20 off the in-phase angle (Fig 51).

Comparing with the measured polar plots of Figs 45 to 48 the positions of

the main beam peaks are:

Beam Measured cos

number peak angle element pattern

2R 450 48.60 41.20

IR 15.50 14.50 13.30

IL -130 -14.5 ° -13.30

2L -42° -48.60 -41.20

The differences are due to the element pattern. The array peak angle

depends upon the shape of the element pattern, in particular, the slope in the

vicinity of the peak of the element pattern. When asymmetry of this element

*t pattern is present the problem is more difficult. In the present case, for

simplification, the element pattern was taken as being cosine shape by matching

slopes around the known location of the experimental maximum. It was difficult

to locate the maximum due to ripples present in the pattern.

The beam nulls resulting from the array pattern (as opposed to the element

pattern) occur at angles which are unaffected by the element pattern shape

(Fig 51).

C.2.2 The position and levels of beam cross-overs for isotropic radiators.

If B is the angular position of the cross-over of the Kth and K + Ithcbeams then, equating the amplitudes of these beams

sin 0c , a (K*I)

A2 rK

Hence 0 - ±300, the cross-over of the first and second beams. The IL, IR -c0

4 beam cross-over occurs at 00.

Appendix C 37

The cross-over level is given by

i I - 0.65

4 " sin( ) 0.

which is approximately -3.7 dB below the peak value, all beams being normalised.

In the dead ahead position the measured element pattern was approximately constant

over the angle of interest and may therefore be assumed isotropic. In the other

cases (given below) the comparison with the above theory is less valid due to the

assumption that the element pattern is cos eLobes Measured In-phase cos e

cross-over angle element pattern

2R + IR +290 +300 27.50

IR + IL +20 00 00

IL + 2L -260 -300 -27.50

In-phase coo eLobes Measured cross-over level

(below peak) element pattern

2R + IR -3.25 dB -3.7 dB -3.25 dB

IR + IL -4.4 dB -3.7 dB -3.25 dB

IL + 2L -3.3 dB -3.7 dB -3.25 dB

*1.

Ao.3

38

Table I

OUTPUT FROM PHASE SHIFTER

DESIGN PROGRAM

DESIGN-01 SEIT G-:1 LOADED LINF PHASE SHIFTERSPHASE "Str - LO6.IE.0 LTNI ADMITTANCES L'NE IFNGTH

-- :-4ttt# LINE LAMBDAS0.000 - 1.0609 1.4579 0.0000

90.0t0 -- .0oo0 1.0000 0.,297DESTGN YF SFT Of 4 LOADED LINE PHASE SHIFTERSPNASt W4f- -L KiNE ADMITTANCES LINE LENGTHDEU ws- -. MIBS LINE LAMBnAS

0.0)O --.,.. -_ -.:. .3 04 .7 270. 0000

.,-o - . 1.,0609 I.,579 0.14619#.WU- _-- _#, - 6719 1.2046 0.3066135.00- . .0 0 00 1.0000 0.7758

DESIO -. LINe PHASE SNIFTERSPHASE fIif:- L-- ADMTTTANCES LYNE LENGTH

- B LINE LAMBDAS43.Oo - 1 ,.jt4 3 1.S398 0.0000

1.7127 0. 0703. - ::i.2301 1.5853 0.1422

-7 * .- ___.- -. -.- 0609 1.1.579 0.216-390.00 : - O.8780 1.3307 0.2938

11250* -- :->0,619 1.2048 0.3769135.0ow . 0. I Z I.0839 0.4705

5- -- -- OfO 1.04.00 0.8460

?p-

Li

39

Table 2

COWUTER REALISATION OF TEST CIRCUITS

R4TESTOI

LARELICOUPLER TEST>;LAREL<MAC SUBSTRATES>;LAREL<VITH END EFFFCTS.>;LARELPFOR DESIGN 4X4 BUTLER/02.>:LAREL<DESIGNED 6/4177.>;OIIEI 16.457E-3 Z50.0 VR.389 ATTO. 1/PI O/P2 CopmMOGLINk2 16.457E-3 AS LINEI I/P7 01P8 COMMONO;LI'JE3 16.458E13 AS LINEI I/P3 O/P4 COMMONO:LINE4 16.45SE-3 AS LItdEl 11P5 O/P6 COMMONO;LIME5 18.723E-3 AS LINE1 I/P2 o/P7 COMMONO;LINE6 18;723E-3 AS L'INEI 11P6 01P3 CONMONO;theE? 17.895E-3 Z35.355 VR.379 ATTO. I/P2 O/P3 COt4MONO;LIeJE8 17.885E-3 AS LINE? I/P? o/P6 CONMONO;SOURCE 50 0;LOAD 50 0;0UTPUT(PR4, IPtVSWRI)iSTFP LIN 1.51E9 1.7E9 0.005E9;

LARELc90 DEGREE P9IASER.>;LARELICMRC SUBRATES.>;LARELCW.ITK END~ EFFECTS.>;LAREL<TEST CIRCUIT,DESIGOED 6/4/77.>:I L14EI 10.734E-3 Z50.0 VR.389 ATTO. h/P1 O/P2 COMMONO;LINE2 22.0F-3 AS LINEI I/P4 O/P6 COMMONObLINE3 18.066E-3 Z41.501 VR..384 ATTO. I/P2 01P4 COMMiONO;LINE4 9.423E-3 Z74.416 VR.403 ATTO. I/P2 O/P3 COMMONO;LINES 9.423E-3 AS LINE4 I/P4 0/P5 COMM1ONk-SO11RCE 50 01LOAD 50 0;OUTPUT(PR4, IPVSWRI);STEP LIN 1.5E9 1.7F9 0.00529;

LARiL135 DEGREE PHASER.>;LAREL<MRC SUBRATE S.>;-LARELICUITH END tFFECTS.>;( LARELICTEST CIRCUIT,DESIGNED 6/4/77.>;LINEI 67.043E-3 Z50.0 VR.389 ATTO. I/Pl 0/P2 COMMONO;SOUJRCE 50 0;LOAD 50 0;OUT PUT (PRA, ! P .VSRI)

STP .Lht -*._I 9 1.72 o.01t_ttSg1.f9

40

Table 3

COMPUTER REALISATION OF COMPLETE BUTLER MATRIX

MBUTW (7)

LAPEL<RUTLER MATRIX.>;LAPEL<WITH END EFFFCTS >;LARE1<I.INE3 AND LTNE? CHANGED TO SEE EFFECT,BOTH CHAN(,FD TO YHF SAMELAAEL<DESN,5/4/7,FOR NRC SUBSTRATES.>: LENGTH.b;LAAEL<FQUjVALENCE OF PORTS.>;LAREL<TNPUTS 1 ,32,17#161lL.2RgiR,2L.>;LAREL(AUTPUTS 10,11 ,27,26=ArCvp#D.>;LINEI 13.0)87E-3 Z50.000 VR.380 ATTO. IPI O/P2 COMMONO;LlwE2 17.885E-3 Z35.355 VR.379 ATTO. I/P2 O/P3 COMMONO:L!NE3 11.228E-3 AS LINFI ZlP3E) O/P4 COMmoFJo;

LINE4 18.066E-3 Z41.501 VR.384 ATTO. I/P4 01P6 COmmONO:L1PJE5 0.423E-3 Z74.416 VR.403 ATTO. J/P4 0/P5 rOMmONO;LINE6 9.423E-3 AS IINF5 !1P6 O1P7 COMMONO;LINE7 11.228E-3 AS LINFI I/P6 O/PZ9 COMMONO;LIhiE8 17.885E-3 AS 111W? U/PS 01P9 COMMONO:LI"'E9 13.087E-3 AS LJ'4F1 1/P9 O/D1O COMMONO;LINEIO 18.723E-3 AS LINEI y/P9 01P12 COMMONO:LIPIEII 18 .72 3E-3 AS LINEI yi/p~ O/P13 COMMONO:LINJE12 13 .08 7F- 3 AS LJNEI I/Pl! 0/PiP COMMONO;LINE13 17.9 8 5 E-3 AS LINE2 I~P12 0/Pl3 commoNO;LINE14 5 6 .7 6 5 E-3 AS LINE1 I/P24 0,P19 COMMONO;LI'JEl5 17.885F-3 AS LINE? 7/Pik O/P15 CoMONO:LIimE16 13.087E-3 AS LT'NEI T/P!5 O/P16 COr4MONO;L!'NE17 13.087E-3 AS ITNEI I/PI7 O/P18 COMMONO;LINE18 18.723E-3 AS LINE1I /PiR 0/P15 COMMONO;LIME19 18.723E-3 AS LINEI 7/Plo fl/P14 COMMONO;LINE20 17.885E-3 AS LINE? I/PIS 01P19 COMMONO;LINEZi 11.4 5 6 E-3 AS LINEI 7/P1. O/P20 COMMONo;LINE22 9.423E-3 AS LINF5 I/P20 O/P21 COMMONO;LINE23 18.066F-3 AS LINE4 I/Pfl O/P22 COMMONO;LINE24 9.423E-3 AS LINF5 I/P2-7 O/P23 COMMONO:LJP'E25 1I.0OO- 3 AS LINOI T/P22 0/P13 COMMONO:LINJE26 18.723E-.3 AS LJNEI T/P2?4 O/P29 COMMONO;LINE27 17.8 8 5E-3 4S LINE2 Y/P//* O/P25 COMMONO;LimE28 13.087E-3 AS LINE1I /P?'5 O/P26 COMMONO:LINIE29 18 .723E-3 AS LINEI T/P25 01P28 COMMONO;LINE30 13.087E-3 As LINE1 I/P2R 01P27 COMMONO:LINE31 17.8 8 5E-3 AS LINE? I/P2 O/P29 COMMONO:LIN4E32 56 .76 5E-3 AS LINEI I/P3 O/P8 COMMONO;L1R9E33 17. 8 8 5E- 3 AS LINE2 10P30 O/P31 COMI40NO;LI'JE34 18 .72 3 E-3 AS LINEI I/P30 O/P3 COMMONO:LIvE35 18.723E-3 AS LINEI T/P31 0/P2 COMMONO:LIpE36 13.087E-3 AS LINEI T/P31 O/P32 COMMONO:SOIPRCF 50 0;VSRLOAD 50 0OUTPUT(PR4,PSR)STPP LIN15E 1.7F9 0,005F9;

41

Table 4a

COMPUTED COUPLER AND PHASE SHIFTER RESULTS AT TRANSMIT,

RECEIVE AND DESIGN FREQUENCIES

T F Rx c x

IR, 1 -11.0 +0.5 +12.5

IR, 2 -101.5 -89.5 -77.5 Coupler phase shift (degrees)

ae -90.5 -90.0 -90.0Phase difference

IR, 1 -3.17 -3.03 -3.01

Coupler insertion loss (dB)

IR, 2 -2.975 -3.00 -3.01

JR, IL 20.75 30.75 30.25 Coupler isolation (dB)

Meanderline -10.25 +0.25 -34.0

90 loaded line -55.0 -44.75 +11.0 Phase shifter phase (degrees)

Pa -44.75 -45.0 -45.0Phase difference

Meanderline 0 0 0

Phase shifter insertion loss (dB)

900 loaded line 0.0012 0 0.0085

I

I

42

Table 4b

MEASURED COUPLER AND PHASE SHIFTER RESULTS AT TRANSMIT,

RECEIVE AND DESIGN FREQUENCIES

T F Rx C X

IR, 1 -39.0 -0.5 +39.5

IR, 2 -130.75 -91.0 -52.0 Coupler phase shift (degrees)

as -91.75 -90.5 -91.5Phase difference

IR, 1 -3.2 -3.15 -3.25

_____ 2_ _ -3.5 _-.3 -45 Coupler insertion loss (dB)

Ii, 2 -3.25 -3.31 -3.45

IR, IL -24.0 -37.75 -25.5 Coupler isolation (dB)

Meanderline -3.0 -45.0 -87.0

900 loaded line +42.5 0 -42.259Phase shifter phase (degrees)

Pa -45.5 -45.0 -44.75Phase difference

900 loaded line 0.15 0.10 0.175 Phase shifter insertion loss (dB)

J 0

43

Table 5

IDEAL PHASE VALUES FOR BUTLER MATRIX (FROt FIG I lb)

COMPARED WITH MEASURED VALUES AT CENTRE FREQUENCY

2 3 4 output port number

input port number IR -45 -90 -135 -180

2L -135 -0 -225 -90

2R -90 -225 0 -135

IL -180 -135 -90 -45

IDEAL

i 2 3 4 output port number

input port number IR 0 -49 -90 -139

2L -91 -320 -!90 -51

2R -47 -178 -316 -87

IL -138 -88 -45 -3.5

SMEASURED

44

Table 6

ERRORS IN PHASE SHIFT (IN DEGREES), MEASURED AND THEORY

TO IDEAL AT TRANSMIT, RECEIVE AND DESIGN FEqUENCIES

I 2 3 4 1 2 3 4

IR 0 -6.0 -1.0 -5.5 IR 0 -0.1 -0.43 -0.12

2L -0.5 -5.5 0 -6.5 2L -0.43 -0.1 +0.5 -0.1 x1.54675 GHz

2R -2.5 +2.0 -1.5 +2.5 2R -0.1 +0.5 -0.1 -0.43

IL -5.5 +1.5 -1.0 -3.5 IL -0.12 -0.43 -0.1 0

1 2 3 4 1 2 3 4

IR 0 -4.0 0 -4.0 IR 0 +0.19 -0.11 +0.2F

2L -1.0 -5.0 0 -6.0 2L -0.11 +0.1 -0.1 +0.19 1.5975 GHz

2R -2.0 +2.0 -1.0 +3.0 2R +0.19 -0.1 +0.1 -0.11

IL -3.0 +2.0 0 -3.5 IL +0.2 -0.11 +0.19 0

1 2 3 4 1 2 3 4

IR 0 -5.0 -1.5 -6.0 IR 0 +0.18 -1.54 +0.1

2L -3.0 -7.0 -2.0 -6.0 2L -1.545 -1.1 +2.4 +0.28 11 .64825 GHz

2R -3.0 +3.5 -3.0 +2.0 2R +0.28 +2.4 -1.; -1.545

IL -4.0 0 -1.0 -2.5 IL +0.1 -1.54 +0.18 0

MEASURED THEORY

af

45

REFERENCES

No. Author Title, etc

I J. Butler Beam-forming Matrix simplifies design of electronically

R. Love scanned antennas.

Eleotronic Design 12, 170-173, April 1961

2 J.R. Wallington Analysis design and performance of a microstrip Butler

Matrix.

European Microwave Conference, Brussels, Vol. 1,

pp A14.3 (1973)

3 P.J. Muenzer Properties of linear phased arrays using Butler

Matrices.

NTZ Heft 9, 419-422 (1972)

4 H.J. Moody The systematic design of the Butler Matrix.

IEEE Trans API2, 786-788, November 1964

5 J. Lange Interdigitated stripline quadrature hybrid.

IEEE Trans HTT 17 (12), 1150-1151, December 1969

6 B.M. Schiffman A new class of broad-band microwave 90 phase shifters.

IRE Trans MTT 6, 232-237, April 1958

7 S. March A wideband stripline hybrid ring.

IEEE Trans MTT 16 (6), p 361, June 1968

8 A. Podell A high directivity microstrip coupler technique.

IEEE G-MTT International Microwave Symposium, 33-36

(1970)

9 B. Easter The equivalent circuit of some microstrip

discontinuities.

IEEE MTT 23 (8), 655-660, August 1975

10 J.R. Wallington Private communication.

Marconi Research Lab. Gt. Baddow

RF TPTs r.1 AV' I~LY(J i Vu COMMERCIAL U!1G,,,IS .

1J

Fig lofb

I

o0---- 20I

3dB

coupler-I 0 -it

0 0 0

Fig la Basic 2 x 2 matrix for broadside Butler matrix

IR

IL. 2

F3dBcoupler

F IR 0 i t

L

i Fig lb Basic 2 x 2 matrix for non-browdside Butler nrix

Fig 2a&b

Arraynormat

Beamdirection

canangle

00 si.-- .___ <.o ,,

"",Lnear hased array "-- , "

I d dl

Fig 2a Phase shift between radiating elements fed by a non-broadside matrix

Arrayaxis

2L IL OdB 1R 2R

:11

,0 l-' IS', o.-,

a ",, .. .. I, _ _d,- . . .a' , a , ,* , .

* ,, ,u; I I

.. .. I_ _. :

I -Ap I ,I I

-600 -400 -200 0 200 40" 60"

Fig 2b Beam widths and positions of 4 element Butler matrix.4r

Fig 3

I

2L'

,2

3

ILI

Fu n

p• Fig 3 Output port configuration

Fig 4

4.406

V4 I-

Ux

UE

ao co 0 co co o a Q 0 0 D 0 D 0 0 D

II

a 0 0) 0 C0 ~ -

U.

40C4(V~-

- if

In w C-

Flp 5-7

Input Isolation

I'j

Coupling Through

Fig 5 The 3 dB Lange coupler

V ., . -- - -- , . VeJ 0

e ! ZI Z, Zoo Zoe ,

- -tan s

Coupled Cos0 , tne= Image impedance line Z tan'O

Zooe Odd mode impedance section

Zoe= Even mode impedance

Fig 6 Schiffman coupler (simplest type)

P input----- " Through PI20

, ' Z o z o l

Isolation Coupling P/2

Fig 7 900 hybrid coupler

Figs 8 9&b

t Through

Isolation zInput

4

Za

Coupled

Fig 8 Wide band 1800 hybrid coupler

Through

Coupling Isolation

Fig 9a Broadside coupler

Input Through

I J

I Coupling Isolation

Fig 9b, Podell coupler

Fig 10afb

Fig 10a Loaded line section

ILL-------

Fig I Ia&b

3

Input Multiples of Outputport is ~ por t

21 2 3

Fig Ile Broadsid4 x 4Butlermbtrix

21. 22 33

R-1 -2 -3 - -1

2L-3 -0 -5,-2.#32R -2 -5 - 3-

Fig lb Non-broedsid 4 x4 Butlernmatrix

Fig 12

2R IL

IR 2L

Fig 12 Alternative layout for 4 x 4 matrix avoiding crossovrs

Fig 13

£09*0

in

oco

4p 0

-4 r

-E*9 - r

40 4

toZT CD

4')

£09*0- £0COO

rSr

-co o0UlV C 0' cgC9

LL4 W1O0l EL~

Fig 14

E-

co2M

Fig1@

IO1350 InsertionPhase loss

dog roes dBZ 74.4 Z74.4 -0.05

120- 2314

I11.228 181.066 1.2

60- 900 Loaded line section

080

1350

2;Z50, --- 50

1350 meander line

-ISO

151.6 1.7Frequency GI~z-

Fig 15a Compufad phas shift and insertion loss for the ust pha shifturs(Ideal lines)

Fig 15b

-10-

-1.671

-1.433

Returnloss -1.307dB

-20- 1.222

900 1.162Loaded line-106

VSWR

-30-

-720 dBMeander line 1.000

1 -Log' (RL x 0.05)

- VSWR z 14.I-pi

-50

1 .5 .61.7Frequency GHz

I- Fig 15b Computed return loss versus frequecy for the tes phas shifters

Fig 16

CouplingIOR,2- -3 dB

120 Isolation

.1Phase RI -20d

degrees

60 -- 30

J-40

IR,2

-600

-es20- hyri couple

Fig 17

-10-

1.671

Return -1.483loss VSWRdB -1.307

-20 -1.222

1.162

1.006

-30-

a0 LogMI. xO.05)

-50

1.5 1.6 1.7* Frequency GHz

Fig 17 Compufmd fein los - all porfs of oouplv %at fcut

Fig 18

Input, outputnumbers

Phase6 IA 1.

degrees

120 -2L. 3; 2R.2

60

02L,2; 2R 3

1R.1; ILA~-60

-120

IR,3; 21.1: 2K4;1L.2

-18 1 ,;II

1.5 1.6 1.7

Frequency GHz

Flo 18 Computed Phas respone of dine Butler matrix .

(input to output port numbers shown)

Fig 19

-10

Return - 1.671

lossdB 1.433

- 1.307

-20 1.222

1.162

1.006

VSWR

-30

P -40 I Log RI L o .05)

VSWR (1 IpI)/(I-lpl)

-50

1.5 1.6 1.7

Frequency GHz

F; Fig 19 Computed return loss versus tfrquency for ill ports of Butler metrix

Fig 20

-7.0

Los~sd8

-6.5+ IR 3; 20 ,

2R.1; iL.3IR11; IL.4

IRA.; IL, I

1 .5 1.s 1.7Frequency GHz

Fi 0Tt opsdls 4uhte einmd C

(iptt uptprsdon

Fig 21

IsolatioridB

-30

1R.21

-20

1 R. IL

-10

01.5 1.6 1.7

Frequency GHz

Fig 21 Coampufad lueon veusfrequecyInput potIR to input, 1 ed 21

Fig 22

-90isolation

dB

-70

-60

1R,2R

1r4 I-50

1.5 1.6 1.7Frequency GHz

R9g22 Computed isolation versus frequency Input port IR to input port2R

Fig 23

RFin

test sot8IAH

out SM

Butter 50 9 loadsmatrix

Fig 23 Gmnerul ut-up for transnilulon memurements

Fig 24

IR.IIPhase IR.2 Coupting d Bdegrees-I-

- 20

60~- 30 Isotation d 8

-le0

I IR

1.5 1.6 1.7

Frequency GI~z

Fig 24 Meaured coupling. isolation and phase shift versus frequency for the ust900 hybrid coupler

Fiji 25

0Insertion loss

120Phase

degrees

60

0

-60

900 loaded section

-120'1350 meander line

-180

'1.5 1.6 1.7* I Frequency GHz

Fig 25 Meuursd insertion loss andl phm shift for fth test phas shifters

Fig 26

1I1 =Log " ' IRL x 0.05)

VSWR = (I.IPI)/(1-IPI)

VSWR

Return 1.671lossdB

1.433

1.307

-20 1.222

1.162

1.006

-30

-40I I

1.5 1.6 1.7

Frequency GHz

F

Fig 26 Measured return loss for 90 ° hybrid coupler. Both inputs

Fig 27

1.671

1. 433

1 . 307

135P-20 90 1.222

Return - 1.162lossdB

- 1.006

VSWR

-30

j II

=Log-1 (RI x 0.05)

VSWR= 1+IpI)I -Ipi

-50

1.5 1.6 V.

Frequency GH z

Fig 27 Measured return Ion versus frequency for the test phase shif ts

Fig 28

Phase IOdegrees

120

60-

0

-60

-120-

2

-1804 13

1.5 1.6 1.7Frequency GHz-

Fig 28 Measured phase shift versus frequency for matrix. Input port 1 R to all outputs

Fig 2

Phasedegrees

120

60-

0-

-602

-120

II-180

31.5 1.6 1.7

Frequency GHz---,-

F

" Fig 29 Memsured phms shift versus frequency for matrix. Input 2L to all outputs

Fig 30

160-

Phasedegrees

120-

2

60-

0-

-60-

e -120-

2 4.

1.5 1.6 1.7Frequency GH z

Fig 30 Measured phase shift versus frequency for matrix. Input port 2R to all outpuU

lFig 31

Phase 2degrees

60

0

-60

-120-

3-10

I 21.5 1.6 1.7

Frequency GHz -

Fi 3

mr " Fig 31 Measured phase shift versus frequency for mitrix. Input port lL to all outputs>1J

Fie 32

-6.0-

LossdB

-7.5

-7.0-

-6.0

151.6 1.7Frequency GZ-

Fig 32 Mmuamd Icas through the matrix. Input port I R to all Output

Fis MI

-7.5-

Lossd B

-7.0-

3

-6.5-

-6.01 I

1.5 1.6 1.7

Fig 33 Measred Ions through the matrix. Input port 21 to all outpuu

Fig 34

Lossd8

-7.5-

2

-7.0- I

-6.50

1. 1. 1.7S

Frequency GHz-

Fig 34 Muuwrsd low through the matrix. Input port 2R to all outpus

LossdB

-7.5-

3

1.5 1.6 1.7

Fig 35 Mimurad loss though the matrix. Input port IL to all outputs

Fig 36

Return

dB

-30 I j

VSWR1.006

1.162

-20- -1.222

-1.307

1.67

I L I L

I I0

1.5 .1.6 1.7Frequency GHz -

I,-

Fig 36 Mesureud return low versus frequency for the matrix. All Inputs

Fig 37

2 R

Isolationd 8

2 L

-101

1.5 1.6 1.7( Frequency GH z -

Fig 37 Measured isolation versu frequency for the matrix. Input port I R to all Inputs

Fig 38

-40L

IsolationdB

30 I I R

0 1.5 1.6 1.7

Frequency GHz

Fig 38 Memred Isdintion versus frequency for the matrix. Input port 2L to all Inputs

Fig 39

I R

Isolationd 8

I L

*01

1.5 1.6 1.7Frequency GHz

Fig 39 Measured Isolation versus frequency for the matrx. Input port 2R to all inputs

Fig 40

Isolattn

2R

1.5 1.6 1.7Frequency GHz-~

Fig 40 Measured isolation versus frequency for the matrix. Input port 1 L to all inputs

Fig 41

Circular microstrip discs

Equal length and impedance microstrip lines

I. ~Feed pt Fee d ptfor RHC for LHC 90' hybrids

pq 41 Skm diegrm of microstrip planar array (all lengths correct at 1.575 GHz)

* Fig 42

Fig 42 Radiation pattern for single element disc antenna

Fig 43

IRI

Bute Polarisationl

Fig 4 ai I t-upof matrix fed array

Recivercabin

Array andfeed

Fig 4 Range mt-up for array nmursnut

Fig 45

IWO

-Fig 45 Poaplot. nul

Fig 46

I IAm"

Fig 46 Polar plot. Input 2R

Fig 47

Fig 47 Polar plot. Input 1 L

Fig 48

Fig4C Polar plot. Input 21

Fig 49 .

d d4

E n E02 Eej I E,-0 E,-0 2 E;E

Fi 4

-'

2

-.

Fig 49Ar- of 2n omni-radlatorsI I-.......... ...... .. .. .. .... .. 111 .. .... ] . ... ...... a . .. ......... ............. .......... ........... ,

Fig 50

2

Fig 0 Diob dymt

Fig 51'

Fig 51 Array theoretical polar diagram - normalilad for assumed cos 0 element patter. . OPin48.60, Op. 14.50

Fig 52

F Expanded array. Theoretical polar diagram for pm 48.60 and anFig 52 Moment pattern of cosr 0 i

demen patm of ci ii

Overall security dluulfcation of this pope

UNCLASSIFIEDI

As far as possble this pqe should contain only unclassified information. Uf it is necessary to enter classifie information, the boxabove must be marked to inicte the classification, eg. Restricted, Confidential or Secret.

I1. DRIC Reference 2. Originator's Reference 3. Agency 4. Report Security ClassificatioQ/Making(to be added by DRIC) RA .T 79118 tmreceUCLASSIzvm

I ~ N/AS. DRIC Code for Originator 6. Originator (Corporate Author) Nam and Location

7673000W Royal Aircraft Establishment, Farnborough, Rants, UK

Sa. Sponsoring Agency's Code 6a. Sponsoring Agency (Contract Authority) Nam and Location

N/A N/A

7. Tite

A thickfilm inicrostrip, Butler Matrix for the frequency range 1.5 -1.7 GHt

7a. (For Translations) ,Title in Foreign Language

7b. (For Conference Papers) Title, Place and Date of Conference

8. Author 1.- Surname, Initials 92. Author 2 9b. Authors 3,4 .... 10. Date Pages Ref.Tabb, A. G. Septemberl 93 1 1

____ ___ ___ ___ ___ __ ___ ___ ____ ___ _ _ ___ ___ ___ ___ ___ 1979

11. Contract Number '12. Period 13. Project 14. Other Reference No.

N/A N/A Space 568

1S. Distribution statement(a) Controfled by - Head of Space Department, RAE (RAL)

(b) *ecl flnftations (if any) -

16. Descriptors (Keywrds) (D~escriptors marked *are selected from TEST)Antsnnas*. Antenna feeds*. Beam forming network. Butler Matrix. Microstrip.

17. AbstractThis Report describes the design, construction and electrical ueasur mnt of

a 4 x 4 Butler Matrix for the 1.5-1.7 G~z frequency range. The Matrix wasconstructed in thickfilm technology on an alumina substrate. A computer aided

"design package vas used f or the circuit synthesis.

-lth